A Multiscale Expectation-Maximization Semisupervised Classifier Suitable for Badly Posed Image Classification

Abstract—This paper deals with the problem of badly posed image classification. Although underestimated in practice, bad-posedness is likely to affect many real-world image classification tasks, where reference samples are difficult to collect (e.g., in remote sensing (RS) image mapping) and/or spatial autocorrelation is relevant. In an image classification context affected by a lack of reference samples, an original inductive learning multiscale image classifier, termed multiscale semisupervised expectation maximization (MSEM), is proposed. The rationale behind MSEM is to combine useful complementary properties of two alternative data mapping procedures recently published outside of image processing literature, namely, the multiscale modified Pappas adaptive clustering (MPAC) algorithm and the sample-based semisupervised expectation maximization (SEM) classifier. To demonstrate its potential utility, MSEM is compared against nonstandard classifiers, such as MPAC, SEM and the single-scale contextual SEM (CSEM) classifier, besides against well-known standard classifiers in two RS image classification problems featuring few reference samples and modestly useful texture information. These experiments yield weak (subjective) but numerous quantitative map quality indexes that are consistent by expert photointerpreters. According to these quantitative results, MSEM is competitive in terms of overall image mapping performance at the cost of a computational overhead three to six times superior to that of its most interesting rival, SEM. More in general, our experiments confirm that, even if they rely on heavy class-conditional normal distribution assumptions that may not be true in many real-world problems (e.g., in highly textured images), semisupervised classifiers based on the iterative expectation maximization Gaussian mixture model solution can be very powerful in practice when: 1) there is a lack of reference samples with respect to the problem/model complexity and 2) texture information is considered negligible (i.e., a piecewise constant image model holds).